As of late I have been researching and trying to figure out calculations regarding the force required by a motor to move a robot that weighs 120 pounds. I understand torque and speed calculations and I can find how fast the wheels (6wd) will spin under no load but i'm not sure how to find how fast they will spin with 120lbs of material atop them.

Top speed is affected by load, but not as much as I'd have thought before getting in to robots. The various FRC calculators, based on a number of measurements and observations, estimate a robot's top speed based on a percentage of the "free" (no load) motor speed, most typically 80% to 85%.

The load will more significantly affect acceleration, especially at startup from a stationary position and in a "pushing match" where the robot is not moving (or only slowly) but applying a force against another robot, field element, or other resistant object. The calculators will take you through this, but approximately:
The motors each draw their "free current" with no benefit other than overcoming friction. Above that point, torque (and therefore applied force on the carpet) is proportional to the current, after multiplicative increases for gearing down and decreases for the wheel radius. Note that a 40A breaker can actually pass 50A for about an FRC match, and rather higher currents for short time periods. Also check out the various curves for your motors - the BAG and CIM style motors can draw stall current for a significant number of seconds before giving up the smoke - but may require cooling between matches, whereas air-cooled motors such as the 775pro cannot draw anywhere near stall for more than a couple of seconds, but can draw current up to the point that they can vent it essentially forever.

Vex has great measurements online for how much current is required to shut down each of the common FRC motors. (click on each motor for the info)

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As of late I have been researching and trying to figure out calculations regarding the force required by a motor to move a robot that weighs 120 pounds. I understand torque and speed calculations and I can find how fast the wheels (6wd) will spin under no load but i'm not sure how to find how fast they will spin with 120lbs of material atop them.

In a frictionless system, the mass would not affect top speed at all, and only change how long it takes the robot to get there. Unfortunately, we don't build frictionless drive trains, and so this question boils down to "how much loss due to friction is there in a fully-loaded robot drive?" The answer to this is, unfortunately, "it's complicated" and your choices are basically to use an arbitrary fudge factor (most people use ~80%), or to test it empirically. Tools like the spreadsheet linked above do the former. The "correct" course of action is the latter.